(at around 20 mins) O'Malley arrives at Lily's apartment. When she answers the door, he discards his newspaper twice between shots.
The conductor mentions to Oliver that Clark is in Drawing Room D; moments later, he tells Oscar that he's in Drawing Room J.
One of the movie magazines seen in a Chicago diner is from February 1934 and on the train that same night Oliver reads a magazine from March 1934, but the dates on the checks Mr. Clark writes on the train are in November 1933.
When Oscar chooses Valerie to replace Lily, there is a POV shot where a middle-aged actress is sitting on a chair between Oscar and Valerie. Then, in a reverse angle shot during continuous action, that actress is standing behind the chair.
When the man kneels in front of Jaffe and calls him Maestro, the position of the man's hands change between shots.
Screenwriter Charles MacArthur's name is used on one of the play posters but is misspelled as "McArthur".
The check that Clark writes to the porter is dated 1933. Working backwards, this establishes that the first act takes place in 1926 and the second in 1929, though the fashions and hairstyles remain very contemporary 1933-1934 throughout the entire film.
When Jaffe takes over direction, he addresses Lily by her new name and she responds, even though she hasn't heard it before. This gap was caused by the deletion of a brief scene in which O'Malley informs her that Jaffe has changed her name.